Op-Amp Inverting/Non-Inverting Calculator

Calculate

Select the op-amp circuit configuration

Feedback resistor in ohms (e.g. 100000 for 100 kΩ). Rf = 0 gives ZERO GAIN (inverting) or UNITY GAIN (non-inverting).

Input resistor in ohms. Signal gain Av = −Rf / Rin.

Resistor tolerance in percent. Used for gain error budget: ε_tol ≈ 2 × tolerance. Leave empty for NOT CHARACTERIZED accuracy class.

Op-amp GBW from datasheet. Used to estimate closed-loop bandwidth: BW = GBW / noise gain.

Bias compensation: Yes (default). Open advanced parameters to change.

Overview

This is a precision-design screening tool for inverting and non-inverting op-amp stages, not a basic gain formula calculator. It computes closed-loop gain in linear and dB form, noise gain (which differs from signal gain in inverting topology and governs bandwidth, stability, and offset propagation), GBW-limited bandwidth, the recommended bias compensation resistor, an output offset estimate from Vos and Ib, and a gain error budget split between resistor tolerance and finite open-loop gain.

A combined status badge classifies the result as a gain band (ZERO / UNITY / ATTENUATION / LOW / MID / HIGH / VERY HIGH) and an accuracy class (PRECISION / GENERAL-PURPOSE / RELAXED / PARTIALLY CHARACTERIZED / NOT CHARACTERIZED), with a separate offset severity sub-line when Vos, Ib, and signal swing are all provided.

The PARTIALLY CHARACTERIZED class is a deliberate honesty signal: when tolerance is entered but A_OL is not, the calculator gives partial screening rather than pretending to know the full error budget. At noise gains above ~100, finite open-loop gain can dominate over resistor tolerance as the error source even with 0.1% precision resistors.

All precision inputs are optional. The calculator produces nominal gain and the bias compensation resistor from just Rf and Rin (or Rg). Each additional input unlocks a deeper layer of the error budget without affecting nominal gain calculation.

How to Use This Calculator

  1. Select the topology — Inverting or Non-Inverting.

  2. Enter the two required resistors — Rf and Rin for inverting, Rf and Rg for non-inverting.

  3. Optionally enter precision-design parameters — Resistor tolerance (%) for the gain error budget; Op-amp open-loop gain A_OL in dB or linear; Input offset voltage Vos and input bias current Ib for output offset estimate; Source impedance Rs if the source is not ideal; Signal swing for offset severity classification; Gain-bandwidth product GBW for closed-loop bandwidth; Indicate whether bias compensation resistor is used.

  4. Click Calculate — read the gain values, the combined status badge, and the offset severity sub-line if applicable.

  5. Check the engineering interpretation — soft checks, gain error budget, and recommended next step.

This calculator covers inverting and non-inverting topologies only. For voltage follower, difference, or summing configurations use the Op-Amp Gain Calculator. All precision inputs are optional — the calculator gives partial screening and flags what is not included in the error budget.

Inputs & Outputs

Inputs

  • •Op-Amp Topology — Options: Inverting, Non-Inverting
  • •Feedback Resistor Rf (Ω)
  • •Input Resistor Rin (Ω)
  • •Ground Resistor Rg (Ω)
  • •Resistor Tolerance (optional) (%)
  • •Open-Loop Gain A_OL (optional)
  • •A_OL Unit — Options: dB, Linear
  • •Input Offset Voltage Vos (optional)
  • •Vos Unit — Options: µV, mV, V
  • •Input Bias Current Ib (optional)
  • •Ib Unit — Options: pA, nA, µA, mA
  • •Source Impedance Rs (optional) (Ω)
  • •Signal Swing (optional)
  • •Signal Swing Unit — Options: mV, V
  • •Gain-Bandwidth Product GBW (optional)
  • •GBW Unit — Options: Hz, kHz, MHz
  • •Bias Compensation Resistor Used — Options: Yes, No

Outputs

  • •Signal Gain Av (signed)
  • •|Av| Magnitude
  • •Gain in dB (dB)
  • •Noise Gain
  • •Closed-Loop Bandwidth (kHz)
  • •Bias Compensation Resistor Rb (Ω)
  • •Output Offset Estimate (mV)

Formula

Calculator Formula

Closed-loop gain is set by external resistors. The topology determines the sign and exact form.

Inverting Amplifier

Av = −Rf / Rin
Av_noise = 1 + Rf / Rin

Signal gain is negative (inverting phase). Noise gain — which governs bandwidth, stability, and offset propagation — is one greater than the signal gain magnitude. This is one of the most common sources of design error.

Non-Inverting Amplifier

Av = 1 + Rf / Rg
Av_noise = Av

Minimum gain is 1 (when Rf = 0). Signal gain equals noise gain. Input impedance is very high.

Derived Quantities

Gain in dB:          Gv_dB = 20 × log₁₀(|Av|)        (undefined when Av = 0)
Closed-loop BW:      BW = GBW / Av_noise               (first-pass mid-band estimate)
Bias compensation:   Rb = Rf ∥ Rin = (Rf × Rin)/(Rf + Rin)  (inverting)
                     Rb = Rf ∥ Rg  = (Rf × Rg)/(Rf + Rg)   (non-inverting)

Rb placement: between non-inverting input and ground (inverting); in series with non-inverting input/source path (non-inverting).

Output Offset Voltage Estimate

Without bias compensation:

Vout_offset = Av_noise × Vos + Av_noise × Ib × R_mismatch
  • Inverting without Rb: R_mismatch = Rf ∥ Rin
  • Non-inverting without source-path Rb: R_mismatch = source impedance Rs

With bias compensation:

Vout_offset ≈ Av_noise × Vos   (Ib contribution largely cancelled)

The residual depends on input offset current Ios (typically 5–10× smaller than Ib) and is described qualitatively.

Gain Error Budget

Tolerance contribution:    ε_tol = 2 × resistor_tolerance
Open-loop gain contribution: ε_AOL = (Av_noise / A_OL_linear) × 100%
Total:                     ε_total = ε_tol + ε_AOL   (linear worst-case sum)

A_OL conversion: A_OL_linear = 10^(A_OL_dB / 20) when dB is selected.

Variables

Symbol Meaning Unit
Av Closed-loop signal gain dimensionless
Av_noise Noise gain (sets BW, stability, offset propagation) dimensionless
Rf Feedback resistor Ω
Rin / Rg Input or ground resistor Ω
GBW Op-amp gain-bandwidth product Hz
BW Estimated closed-loop bandwidth Hz
Rb Bias compensation resistor Ω
Vos Input offset voltage V
Ib Input bias current A
A_OL Open-loop gain dB or linear
ε_tol Gain error from resistor tolerance %
ε_AOL Gain error from finite open-loop gain %

Status Classification

Track A — Gain magnitude (primary badge):

Status |Av| Typical Use
ZERO GAIN = 0 Feedback resistor is zero
UNITY GAIN = 1 Buffer, isolation stage
ATTENUATION 0 – 1 Inverting only; Rf < Rin
LOW GAIN 1 – 10 Sensor preamps, audio front-ends
MID GAIN 10 – 100 Instrumentation, strain gauges
HIGH GAIN 100 – 1000 Low-level sensors, precision front-ends
VERY HIGH GAIN > 1000 Multi-stage recommended

Track B — Accuracy class (combined badge):

Class Condition
NOT CHARACTERIZED Tolerance not entered
PARTIALLY CHARACTERIZED Tolerance entered, A_OL not entered
PRECISION ε_total < 1%
GENERAL-PURPOSE 1% ≤ ε_total < 5%
RELAXED ε_total ≥ 5%

Track C — Offset severity (sub-line, when Vos, Ib, and signal swing all entered):

Sub-status Condition
LOW OFFSET IMPACT Vout_offset < 1% of signal swing
MODERATE OFFSET IMPACT 1% ≤ Vout_offset < 5% of signal swing
HIGH OFFSET IMPACT Vout_offset ≥ 5% of signal swing

What is the Difference Between Inverting and Non-Inverting Op-Amp Configurations?

The two topologies differ in which input receives the signal and how feedback sets the gain. In the inverting configuration, the signal enters through Rin to the inverting (−) input, and Rf provides feedback from output to that same node. The non-inverting (+) input is held at reference ground. The closed-loop gain is Av = −Rf/Rin, with the negative sign indicating 180° phase inversion. Input impedance is approximately Rin, which can be a constraint for high-impedance sources. Noise gain (1 + Rf/Rin) is one greater than signal gain magnitude — this distinction governs bandwidth, stability, and the propagation of input offset voltage to the output.

In the non-inverting configuration, the signal enters directly at the non-inverting input, and feedback is taken from the output through the Rf-Rg divider to the inverting input. The closed-loop gain is Av = 1 + Rf/Rg, which is always positive and at least 1. Input impedance is very high — effectively the op-amp's differential input impedance, often in the gigaohm range. Signal gain equals noise gain. Both topologies share the same precision-design considerations: resistor tolerance, finite op-amp open-loop gain, input offset voltage, input bias current, and source impedance all influence accuracy and DC offset.

Bias Compensation and Output Offset

Input bias current (Ib) flows through the source impedance seen by each op-amp input. If the two input paths present unequal impedance, Ib creates unequal voltage drops and an output offset equal to Av_noise × Ib × R_mismatch. A bias compensation resistor Rb — equal to Rf ∥ Rin for inverting, or Rf ∥ Rg for non-inverting — balances the impedance seen by both inputs. With Rb in place, the bias-current contribution reduces from Ib to Ios (input offset current), which is typically 5–10× smaller. Input offset voltage Vos is multiplied by noise gain regardless of Rb and remains the dominant offset term in precision designs.

For DC-sensitive applications, the total output offset at high gain can easily exceed the signal swing. A stage with Av_noise = 100, Vos = 1 mV, and Ib = 50 nA without bias compensation and with 600 Ω source impedance produces an output offset of about 100 mV + 3 mV = 103 mV. Against a 2 V signal swing, that is 5.15% — classified as HIGH OFFSET IMPACT. Using a lower-Vos op-amp or adding Rb reduces the dominant terms systematically.

Gain Error Budget: Tolerance and Open-Loop Gain

Gain accuracy depends on two primary error sources that this calculator evaluates independently. Resistor tolerance contributes approximately 2 × tolerance (worst-case screening for simple ratio topologies). With 1% resistors, the tolerance contribution is around 2%. Finite open-loop gain A_OL contributes (Av_noise / A_OL_linear) × 100%. For a standard 100 dB op-amp (A_OL_linear = 100,000) at noise gain 100, the A_OL contribution is 0.1% — comparable to using 0.05% precision resistors.

At high noise gain, the A_OL contribution can dominate. A 100 dB op-amp at noise gain 1000 contributes 1% gain error from A_OL alone — larger than the tolerance contribution from 0.1% resistors (0.2%). The PARTIALLY CHARACTERIZED accuracy class flags this condition: when A_OL is not entered, the calculator shows the tolerance contribution but cannot assess whether A_OL is the larger error. Entering A_OL from the op-amp datasheet completes the budget and resolves the accuracy class to PRECISION, GENERAL-PURPOSE, or RELAXED.

Key Facts

  • Inverting amplifier signal gain is Av = −Rf/Rin; non-inverting is Av = 1 + Rf/Rg. The non-inverting topology cannot produce attenuation — its minimum gain is 1.
  • In inverting topology, signal gain and noise gain differ: Av = −Rf/Rin but Av_noise = 1 + Rf/Rin. Bandwidth, stability, and DC offset propagation are governed by noise gain, not signal gain. This is one of the most common sources of design error.
  • The bias compensation resistor (Rb = Rf ∥ Rin for inverting, Rb = Rf ∥ Rg for non-inverting) cancels most of the DC offset from input bias current. The residual depends on input offset current Ios, typically 5–10× smaller than Ib.
  • Output offset combines two amplified contributions: Av_noise × Vos plus Av_noise × Ib × R_mismatch. Both grow with noise gain — at high gain the output offset can exceed the intended signal swing.
  • Finite open-loop gain creates an error of (Av_noise / A_OL) × 100%. At noise gains above ~100, this can equal or exceed the resistor tolerance contribution even with 1% resistors.
  • For voltage-feedback op-amps with dominant-pole compensation, closed-loop bandwidth is approximately GBW divided by noise gain. Doubling gain halves bandwidth.
  • Resistor preferred values follow IEC 60063: E12 (10%), E24 (5%), E48 (2%), E96 (1%), E192 (0.5% / 0.25% / 0.1%).
  • For simple ratio topologies, worst-case gain error from resistor tolerance is roughly 2 × tolerance. With 1% resistors, gain accuracy from tolerance alone is around 2%.

Applications

  • Audio preamplifiers and microphone front-ends, typically in the LOW to MID GAIN range.
  • Sensor signal conditioning for thermocouples, strain gauges, photodiodes, and accelerometers.
  • Instrumentation front-ends where gain accuracy below 1% is required.
  • DC-coupled buffers where input offset voltage and bias current must be analysed for output accuracy.
  • Photodiode current-to-voltage conversion in inverting configuration with high Rf.
  • Screening whether resistor tolerance or finite open-loop gain is the dominant source of closed-loop error before selecting an op-amp.
  • Verifying whether a gain target is achievable with practical resistor values, given a specific op-amp's A_OL and Vos.
  • Educational use for teaching feedback theory, the distinction between signal gain and noise gain, and the role of bias compensation.

Example Calculation

Example 1 — Precision Sensor Frontend, Inverting with Bias Compensation

Inputs:

  • Topology: Inverting
  • Rf = 100 kΩ, Rin = 10 kΩ
  • Tolerance = 0.1%, A_OL = 120 dB
  • Vos = 100 µV, Ib = 5 nA
  • Bias compensation: Yes
  • Signal swing = 5 V

Calculation:

Av = −100000 / 10000 = −10
|Av| = 10, Av_noise = 11
Rb = (100000 × 10000) / (100000 + 10000) = 9090.9 Ω ≈ 9.09 kΩ
Vout_offset = 11 × 100 µV = 1.1 mV  (bias term largely cancelled by Rb)
ε_tol = 2 × 0.1% = 0.2%
ε_AOL = (11 / 10^6) × 100% = 0.0011%
ε_total = 0.201% → PRECISION
Offset severity = 1.1 mV / 5 V = 0.022% → LOW OFFSET IMPACT

Result:

  • Badge: LOW GAIN / PRECISION
  • Sub-line: Offset severity: LOW OFFSET IMPACT
  • Dominant error source: resistor tolerance

Example 2 — General-Purpose Audio Preamp, Non-Inverting

Inputs:

  • Topology: Non-Inverting
  • Rf = 99 kΩ, Rg = 1 kΩ
  • Tolerance = 1%, A_OL = 100 dB
  • Vos = 1 mV, Ib = 50 nA
  • Bias compensation: No, Rs = 600 Ω
  • Signal swing = 2 V

Calculation:

Av = 1 + 99000 / 1000 = 100, Av_noise = 100
Rb_recommended = (99000 × 1000) / (99000 + 1000) = 990 Ω
Vout_offset = 100 × 1 mV + 100 × 50 nA × 600 Ω = 100 mV + 3 mV = 103 mV
ε_tol = 2%, ε_AOL = (100 / 100000) × 100% = 0.1%
ε_total = 2.1% → GENERAL-PURPOSE
Offset severity = 103 mV / 2 V = 5.15% → HIGH OFFSET IMPACT

Result:

  • Badge: MID GAIN / GENERAL-PURPOSE
  • Sub-line: Offset severity: HIGH OFFSET IMPACT
  • Dominant error source: resistor tolerance
  • Note: Offset impact is high — consider adding Rb = 990 Ω or using a lower-Vos op-amp.

Example 3 — Inverting Attenuation

Inputs:

  • Topology: Inverting
  • Rf = 1 kΩ, Rin = 10 kΩ, Tolerance = 5%

Calculation:

Av = −1000 / 10000 = −0.1, |Av| = 0.1, −20 dB
Av_noise = 1 + 0.1 = 1.1
ε_tol = 2 × 5% = 10% → RELAXED

Result:

  • Badge: ATTENUATION / RELAXED
  • Note: Even in attenuation, noise gain (1.1) still amplifies Vos and Ib at the output.

Standards & References

  • IEC 60063:2015 — Preferred number series for resistors and capacitors. Defines the E-series (E3, E6, E12, E24, E48, E96, E192). Official IEC page.
  • IEC 60062 — Marking codes for resistors and capacitors. Companion standard for IEC 60063.
  • Analog Devices, "Op Amp Applications Handbook" — Comprehensive practical reference for inverting, non-inverting, and precision design topics. Freely available.
  • Texas Instruments, "Op Amps for Everyone" — Design handbook covering bias compensation, offset, and gain accuracy.
  • JEDEC Standards — Standards for semiconductor parameter definitions, including op-amp characterization terminology (Vos, Ib, Ios, A_OL, GBW).
  • Horowitz & Hill, "The Art of Electronics" (3rd edition, Cambridge University Press) and Sedra & Smith, "Microelectronic Circuits" — Standard textbook references for op-amp configurations and feedback theory.
  • Full IEC standards are purchased through the IEC webstore. Analog Devices and Texas Instruments handbooks are freely available online.

Units

This calculator uses SI-derived electrical units that are universal across regions:

  • Resistance — ohms (Ω), with prefixes kΩ and MΩ
  • Voltage — volts (V), with prefixes mV and µV
  • Current — amperes (A), with prefixes mA, µA, nA, pA
  • Frequency — hertz (Hz), with prefixes kHz and MHz
  • Gain — dimensionless ratio (linear) and decibels (dB)
  • Tolerance — percent (%)

There is no Imperial alternative — electrical units are the same worldwide. A 4.7 kΩ resistor and a 100 MHz op-amp have identical meaning on any datasheet regardless of country.

Open-loop gain A_OL accepts both dB (typical datasheet format, e.g. 100 dB) and linear (e.g. 100,000) via a unit selector. Internal calculation always uses linear: A_OL_linear = 10^(A_OL_dB / 20).

Limitations

  • This calculator covers inverting and non-inverting topologies only. For voltage follower, difference, or summing configurations, use the Op-Amp Gain Calculator.
  • Closed-loop bandwidth is a first-pass mid-band estimate from GBW and noise gain. It is not a substitute for datasheet AC analysis, phase-margin review, or simulation.
  • Output offset estimate is a worst-case screening, not a precise DC simulation. PSRR, CMRR, temperature drift, and 1/f noise are not modelled.
  • The bias compensation residual (after applying Rb) depends on input offset current Ios, which is not a calculator input. The model describes the reduction qualitatively but does not solve numerically.
  • Gain error budget is a linear worst-case sum of the entered contributions. Real statistical error is typically smaller (RSS sum) and is not produced.
  • The calculator does not check whether the required output swing fits within the op-amp supply rails.
  • A_OL is treated as a single DC value; its frequency rolloff is captured only indirectly through GBW and bandwidth.
  • Temperature coefficient of resistors and op-amp drift over temperature are not modelled.

Common Mistakes to Avoid

  • Confusing signal gain with noise gain in inverting topology. Av = −Rf/Rin sets signal amplification, but Av_noise = 1 + Rf/Rin governs bandwidth, stability, and offset propagation.
  • Trying to achieve gain below 1 with a non-inverting amplifier. The minimum non-inverting gain is 1; for attenuation, use the inverting topology with Rf < Rin.
  • Skipping the bias compensation resistor in inverting topology when input bias current is significant. The resistor adds no signal-path complication and cancels most of the bias-current offset.
  • Skipping the impedance balance in non-inverting topology when source impedance is non-zero. Without it, bias current creates offset proportional to source impedance.
  • Treating the 2 × tolerance gain error as a strict bound. It is a worst-case screening estimate for simple ratio topologies, not a guaranteed limit.
  • Ignoring finite open-loop gain at high noise gain. At Av_noise above 100, A_OL contribution can equal or exceed the resistor tolerance contribution. Always include A_OL in the budget for precision design.
  • Selecting an op-amp by GBW alone. Vos drift, Ib drift, noise density, and Ios all matter for precision DC accuracy.
  • Designing single-stage amplifiers above 1000× gain. Cascading two moderate-gain stages typically gives better bandwidth, lower noise, and lower DC offset.

Frequently Asked Questions

What is the formula for inverting op-amp gain?
Inverting amplifier signal gain is Av = −Rf / Rin. The negative sign indicates 180° phase inversion. Noise gain is 1 + Rf / Rin, which sets bandwidth and stability. Closed-loop bandwidth is GBW divided by noise gain.
What is the formula for non-inverting op-amp gain?
Non-inverting amplifier gain is Av = 1 + Rf / Rg, where Rg is the resistor from the inverting input to ground. The minimum gain is 1, achieved when Rf = 0. Signal gain equals noise gain in this topology.
How do I calculate the op-amp bias compensation resistor?
The bias compensation resistor balances the DC source impedance seen by the two op-amp inputs. For inverting topology, Rb = Rf ∥ Rin = (Rf × Rin) / (Rf + Rin), placed between the non-inverting input and ground. For non-inverting topology, Rb = Rf ∥ Rg = (Rf × Rg) / (Rf + Rg), placed in series with the non-inverting input/source path. With Rb matched, the bias-current contribution to output offset reduces from Ib to Ios, typically 5–10× smaller.
How do I estimate op-amp output offset voltage?
Output offset is Av_noise × Vos + Av_noise × Ib × R_mismatch, where R_mismatch is the imbalance between the two input paths. For inverting without Rb: R_mismatch = Rf ∥ Rin. For non-inverting without bias compensation: R_mismatch = source impedance Rs. With bias compensation applied, the bias-current term is largely cancelled and the residual scales with Ios.
Why is noise gain higher than signal gain in inverting topology?
Signal gain in inverting topology is Av = −Rf/Rin. Noise gain is what the op-amp's inverting input sees back to the output: a non-inverting divider with the same resistor pair, giving 1 + Rf/Rin. The two values differ by exactly 1. Noise gain — not signal gain — determines closed-loop bandwidth (BW = GBW / Av_noise), stability margins, and how much input offset voltage Vos appears at the output.
When does open-loop gain affect closed-loop accuracy?
Closed-loop gain accuracy depends on the ratio of noise gain to open-loop gain A_OL. The error contribution is (Av_noise / A_OL) × 100%. At low gain (Av_noise < 10) and standard A_OL (100 dB = 100,000), this contribution is below 0.01% and negligible. At Av_noise above 100, the contribution can equal or exceed resistor tolerance error. For precision design above noise gain ~50, always include A_OL in the error budget.
What does PARTIALLY CHARACTERIZED mean?
PARTIALLY CHARACTERIZED is the accuracy class shown when resistor tolerance is entered but A_OL is not. The calculator can compute the tolerance contribution to gain error but cannot include the open-loop gain contribution. At noise gains above ~100, A_OL can be the dominant error source even with tight resistors. Enter A_OL (in dB or linear) to upgrade to PRECISION, GENERAL-PURPOSE, or RELAXED based on the complete budget.
How do I choose between inverting and non-inverting topology?
Inverting offers virtual-ground summing, accepts gain below 1 (attenuation), and inverts the output phase. Its input impedance equals Rin, which can load high-impedance sources. Non-inverting has very high input impedance (good for sensors and high-impedance sources), preserves signal phase, but cannot attenuate (minimum gain is 1). Both topologies need bias compensation for precision DC accuracy when input bias current is significant.

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